The Rayleigh criterion specifies the minimum separation between two incoherent point sources that may be resolved into distinct objects. We revisit this problem by examining Fisher information required for resolving sources. resulting Cramer–Rao bound gives error achievable any unbiased estimator. When only intensity in image plane is recorded, diverges as tends to zero, an effect has been dubbed curse. Nonetheless, curse can lifted with suitable measurements. Here, we work out optimal...

We present, and analyze thoroughly, a highly symmetric efficient scheme for the determination of single-qubit state, such as polarization properties photons emitted by single-photon source. In our there are only four measured probabilities, just enough three parameters that specify qubit whereas standard procedure would measure six probabilities.

A general protocol in quantum information and communication relies the ability of producing, transmitting, reconstructing, general, qunits. In this Letter we show for first time experimental implementation these three basic steps on a pure state three-dimensional space, by means orbital angular momentum photons. The reconstruction qutrit is performed with tomographic techniques maximum-likelihood estimation method. For used more than 2400 different projections. way also demonstrate that can...

We propose a refined iterative likelihood-maximization algorithm for reconstructing quantum state from set of tomographic measurements. The is characterized by very high convergence rate and features simple adaptive procedure that ensures likelihood increase in every iteration to the maximum-likelihood state. apply homodyne tomography optical states entangled spin trapped ions investigate its properties.

We establish the multiparameter quantum Cram\'er-Rao bound for simultaneously estimating centroid, separation, and relative intensities of two incoherent optical point sources using alinear imaging system. For equally bright sources, is independent source which confirms that Rayleigh resolution limit just an artifact conventional direct can be overcome with adequate strategy. general case unequally amount information one gain about separation falls to zero, but we show there always a...

We introduce an operator linked with the radial index in Laguerre-Gauss modes of a two-dimensional harmonic oscillator cylindrical coordinates. discuss ladder operators for this variable, and confirm that they obey commutation relations su(1,1) algebra. Using fact, we examine how basic quantum optical concepts can be recast terms modes.

We revisit the application of neural networks to quantum state tomography. confirm that positivity constraint can be successfully implemented with trained convert outputs from standard feed-forward valid descriptions states. Any neural-network architecture adapted our method. Our results open possibilities use state-of-the-art deep-learning methods for reconstruction under various types noise.

The quantum Cramér-Rao bound (QCRB) stands as a cornerstone of metrology. Yet, akin to its classical counterpart, it provides only local information and overlooks higher-order details. We leverage the theory asymptotics circumvent these issues, providing corrections performance estimators beyond QCRB. While QCRB often yields whole family optimal states several measurements, our approach allows us identify measurements within that are otherwise equivalent according alone; requisite for...

We show first reconstructions of the photon-number distribution obtained with a multichannel fiber-loop detector. Apart from analyzing statistics light pulses this device can serve as sophisticated postselection for experiments in quantum optics and information. quantify its efficiency by means Fisher information compare it to ideal photodetector.

Quantum-state reconstruction on a finite number of copies quantum system with informationally incomplete measurements, as rule, does not yield unique result. We derive scheme where both the likelihood and von Neumann entropy functionals are maximized in order to systematically select most-likely estimator largest entropy, that is, least-bias estimator, consistent given set measurement data. This is equivalent joint consideration our partial knowledge ignorance about ensemble reconstruct its...

We establish the conditions to attain ultimate resolution predicted by quantum estimation theory for case of two incoherent point sources using a linear imaging system. The solution is closely related spatial symmetries detection scheme. In particular, real symmetric spread functions, any complete set projections with definite parity achieves goal.

By projecting onto complex optical mode profiles, it is possible to estimate arbitrarily small separations between objects with quantum-limited precision, free of uncertainty arising from overlapping intensity profiles. Here we extend these techniques the time-frequency domain using mode-selective sum-frequency generation shaped ultrafast pulses. We experimentally resolve temporal and spectral incoherent mixtures single-photon level signals ten times smaller than their bandwidths a tenfold...

An iterative algorithm for the reconstruction of an unknown quantum state from results incompatible measurements is proposed. It consists Expectation-Maximization step followed by a unitary transformation eigenbasis density matrix. The procedure has been applied to entangled pair photons.

We report on an intrinsic relationship between the maximum-likelihood quantum-state estimation and representation of signal. A quantum analogy transfer function determines space where reconstruction should be done without need for any ad hoc truncations Hilbert space. An illustration this method is provided by a simple yet practically important tomography optical signal registered realistic binary detectors.

It has been argued that, for a spatially invariant imaging system, the information one can gain about separation of two incoherent point sources decays quadratically to zero with decreasing separation.The effect is termed Rayleigh's curse.Contrary this belief, we identify class point-spread functions (PSFs) linear decrease.Moreover, show that any well-behaved symmetric PSF be converted into such form simple nonabsorbing signum filter.We experimentally demonstrate significant superresolution...

We construct optimal measurements, achieving the ultimate precision predicted by quantum theory, for simultaneous estimation of centroid, separation, and relative intensities two incoherent point sources using a linear optical system. discuss physical feasibility scheme, which could pave way future practical implementations quantum-inspired imaging.

Quantum state tomography is both a crucial component in the field of quantum information and computation formidable task that requires an incogitable number measurement configurations as system dimension grows. We propose experimentally carry out intuitive adaptive compressive scheme, inspired by traditional compressed-sensing protocol signal recovery, tremendously reduces needed to uniquely reconstruct any given without additional priori assumption whatsoever (such rank information, purity,...

In recent proposals for achieving optical super-resolution, variants of the Quantum Fisher Information (QFI) quantify attainable precision. We find that claims about a strong enhancement resolution resulting from coherence effects are questionable because they refer to very small subsets data without proper normalization. When QFI is normalized, accounting strength signal, there no advantage coherent sources over incoherent ones. Our findings have bearing on further studies achievable...

We propose a numerical algorithm for finding optimal measurements quantum-state discrimination. The theory of the semidefinite programming provides simple check optimality numerically obtained results. With help our we calculate minimum attainable error rate device discriminating between three particularly chosen pure qubit states.

We build an operational scheme for the quantum state reconstruction based on fitting of data patterns. Each pattern corresponds to response measurement setup a predefined reference state. The set patterns can be measured experimentally in calibration stage preceding reconstruction. quorum states plays role positive operator valued measure terms which is done. As main advantage, procedure free notorious problems with projections into non-normalizable quadrature eigenstates, infinite...

Quantum metrology allows for a tremendous boost in the accuracy of measurement diverse physical parameters. The estimation rotation constitutes remarkable example this quantum-enhanced precision. recently introduced Kings Quantumness are especially germane task when axis is unknown, as they have sensitivity independent that and achieve Heisenberg-limit scaling. Here, we report experimental realization these states by generating up to 21-dimensional orbital angular momentum single photons,...

We show that, contrary to popular belief, non only diffraction-free beams may reconstruct themselves after hitting an opaque obstacle but also, for example, Gaussian beams.We unravel the mathematics and physics underlying self-reconstruction mechanism we provide a novel definition minimum reconstruction distance beyond geometric optics, which is in principle applicable any optical beam that admits angular spectrum representation.Moreover, propose quantify ability of via newly established...

Because any unitary operation is a rotation, in sense measuring rotation the most universal sort of measurement. In practice, precise measurements are essential, from magnetometry to inertial navigation fundamental tests physics. The ultimate limits for simultaneously all components dictated by quantum theory, and here tested using light's orbital angular momentum multiplane light conversion. Rotated states projected onto set coherent deduce parameters, method inspired GPS. results near precision.